A functional approach to the numerical conformal bootstrap

• Main Authors: Miguel F. Paulos, Bernardo Zan
• Format: Article
• Language: English
• Published: SpringerOpen 2020-09-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Field Theories in Lower Dimensions; Nonperturbative Effects
• Online Access: http://link.springer.com/article/10.1007/JHEP09(2020)006

Abstract We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of bound-saturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.